Prove the below theorem: Let Y, and Y, denote random variables. Then E(Y;) = E[E(Y;|Y2)], where on the right-hand side the inside expectation is with respect to the conditional distribution of Y, given Y2 and the outside expectation is with respect to the distribution of Y,.
Prove the below theorem: Let Y, and Y, denote random variables. Then E(Y;) = E[E(Y;|Y2)], where on the right-hand side the inside expectation is with respect to the conditional distribution of Y, given Y2 and the outside expectation is with respect to the distribution of Y,.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 43CR
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![Question 3
Prove the below theorem:
Let Y, and Y, denote random variables. Then
E(Y;) = E[E(Y,|Y2)],
where on the right-hand side the inside expectation is with respect to the conditional
distribution of Y, given Y, and the outside expectation is with respect to the distribution of Y2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd99cdbf1-36f1-4d9b-8fb4-5c640c5f48c0%2F98a709f4-ffda-42c4-b141-260838264b3d%2Fktl2vte_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 3
Prove the below theorem:
Let Y, and Y, denote random variables. Then
E(Y;) = E[E(Y,|Y2)],
where on the right-hand side the inside expectation is with respect to the conditional
distribution of Y, given Y, and the outside expectation is with respect to the distribution of Y2.
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